Wavelet based approach for joint time delay and Doppler stretch measurements

A new wavelet-based algorithm for joint time delay and Doppler stretch estimation in passive radar, sonar, and GPS applications is described. By taking the cross wavelet transform of the noisy outputs from two spatially separated sensors, the wideband cross ambiguity function (WBCAF) can be computed. This in turn provides a direct measurement of the time difference and Doppler stretch between the two signals. The Cramer-Rao lower bound (CRLB) is derived and the performance of the proposed algorithm is analyzed. It is found that the theoretical variances of the estimates are unbiased and approach the CRLB at high signal-to-noise ratio (SNR). In order to improve the accuracy of the estimation under noisy environment, a simple denoising method is introduced. Simulation results are given to corroborate the analysis.

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